The invention relates to a process for remelting metal surfaces using a laser to increase the wear resistance of metal surfaces. This is of particular importance in the case of camshafts which are used for the valve timing gear in internal-combustion engines. Due to their rotary movement, the individual cams arranged on the camshaft effect an adjustment of the corresponding cam followers, valve levers or the like. Normally, the wear resistance of the cam running surfaces is increased by remelting. It has already been known for a relatively long time to make use of the so-called TIG process (tungsten inert gas process) for this purpose. A particular disadvantage of this process is, the relatively high time outlay and the long cycle times bound up therewith. German Publication DE 3,916,684 A1 discloses using a rectangular laser beam to carry out remelting of valve lever running surfaces for the valve timing gear of internal-combustion engines. The width of the surfaces to be remelted is subdivided there into a plurality of subregions and a large middle top region is remelted separately in time from outer edge regions. Here, too, the time outlay is still relatively high.